Solve the equation: 3m² + 2m - 7 = 0

To solve the quadratic equation \(3m² + 2m - 7 = 0\), we can use the quadratic formula, which is given by:

Quadratic Formula

The formula is:

m = (-b ± √(b² - 4ac)) / 2a

In this equation, \(a = 3\), \(b = 2\), and \(c = -7\).

Step 1: Calculate the Discriminant

The discriminant is calculated as:

b² - 4ac

Substituting the values:

2² - 4(3)(-7) = 4 + 84 = 88

Step 2: Apply the Quadratic Formula

Now, plug the values into the quadratic formula:

m = (-2 ± √88) / (2 * 3)

Since \(√88\) can be simplified to \(2√22\), the equation becomes:

m = (-2 ± 2√22) / 6

Step 3: Simplify the Expression

This can be further simplified:

m = (-1 ± √22) / 3

Final Solutions

The solutions for the equation \(3m² + 2m - 7 = 0\) are:

• m = (-1 + √22) / 3
• m = (-1 - √22) / 3